The Vector Field Histogram

Erick TryzelaarNovember 14, 2001Robotic Motion Planning

A Method Developed by J. Borenstein and Y. Koren

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The Problem To simultaneously:

Detect, and avoid, unknown obstacles in real-time

Steer in the best direction that leads to some target, ktarg

Do it as quickly as possible

Robot

ktarg

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The Solution: The Vector Field Histogram (VFH) The first step generates

a 2D Cartesian coordinate from each range sensor, and increments that position in the histogram grid C

Note: this method does not depend on a specific sensor model

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Robot

Histogram Grid, C

ktarg

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The Solution, Continued (2) The next step filters this two

dimensional grid down into a one dimensional structure

The final step calculates the steering angle and the velocity controls from this structure

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First, Some Terminology VCP

The center point of the robot

Obstacle vector A vector pointing from a

cell in C* to the VCP

VCP

Robot

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3 1 4 2 13 3 4 5 1 1

Robot

Obstacle Vector

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Step 2: Mapping 2D onto 1D In order to simplify

calculations, the 2D grid used in this step is a window of C, with constant dimensions, and centered on the VCP, called the active grid, or C*.

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3 1 4 2 13 3 4 5 1 14 5 3

Robot

Active Grid, C*

ktarg

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Step 2: Continued (2) This is then mapped

onto a 1D structure known as a polar histogram, or H. A polar histogram is a one-dimensional grid comprising of n angular sections with width

Figure included with permission from J. Borenstein

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3 1 4 2 13 3 4 5 1 14 5 3

Robot

Active Grid, C*

ktarg

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Step 2: Continued (3) In order to generate H, we must first map every

cell in C* onto a 1D point in H’s coordinate system

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Step 2: Continued (4)

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Figure included with permission from J. Borenstein

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Step 2: Continued (5) Because H at this point contains

discrete points, a smoothing function can be applied in order to better approximate the environment

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Step 3: Computing the Steering Direction A typical polar

histogram contains “peaks”, or sectors with a high polar obstacle density (POD), and “valleys”, sectors that contain low POD’s

A valley below some threshold is called a candidate valley

Figure included with permission from J. Borenstein

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Step 3: Continued (2) From all the candidate

valleys, the valley closest to the ktarg is selected

The type of the valley is dependant on the some consecutive number of sectors, Smax, under the threshold Wide is greater than Smax

Narrow is less than Smax

Robot

ktarg

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Step 3: Continued (3) In that valley, kn is selected

from the first or the last sector, whichever is closer to ktarg

Wide valleys: kf = kn ± Smax, which results in kf in the valley

Narrow valleys: kf is the last sector in the valley

Then = (kn + kf)/2

Robot

ktarg

kn

kf

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Step 3: Selecting the Threshold

If set too high, the robot may be too close to an obstacle, and moving too quickly in order to prevent a collision

However, if set too low, VFH can miss some valid candidate valleys

Generally, the threshold does not need much tuning, unless the application of the robot requires very fast navigation of tightly packed obstacles

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Step 3: Speed Controls

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Comparison to Potential Fields Influences of a bad sensor read is minimized because it is

averaged out with prior data

Instability in traveling down a narrow corridor is eliminated because the polar histogram varies only slightly between sonar reads

The “repulsive forces” from obstacles cannot counterbalance the “attractive force” from the target and trap the robot in a local minima, as VFH only tries to drive through the best possible valley, regardless if it leads away from the target

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Comparison, Continued (2) However, VFH can not

solve all the limitations inherent with the potential field method Nothing prevents the robot

from being caught in a real local minima, or a cycle

When this occurs, a global path planner must be used to generate intermediary targets for the VFH until it is out of the trap

Robot

ktarg